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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 10, Iss. 5 — May. 1, 1993
  • pp: 1078–1085

Maximum a posteriori estimation with Good’s roughness for three-dimensional optical-sectioning microscopy

Sarang Joshi and Michael I. Miller  »View Author Affiliations


JOSA A, Vol. 10, Issue 5, pp. 1078-1085 (1993)
http://dx.doi.org/10.1364/JOSAA.10.001078


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Abstract

The three-dimensional image-reconstruction problem solved here for optical-sectioning microscopy is to estimate the fluorescence intensity λ(x), where x3, given a series of Poisson counting process measurements { M j ( d x ) } j = 1 J, each with intensity sj(y) ∫3pj(y|x)λ(x)dx, with pj(y|x) being the point spread of the optics focused to the jth plane and sj(y) the detection probability for detector pointy at focal depth j. A maximum a posteriori reconstruction generated by inducing a prior distribution on the space of images via Good’s three-dimensional rotationally invariant roughness penalty ∫3 [|Δλ(x)|2/λ(x)]dx. It is proven that the sequence of iterates that is generated by using the expectation maximization algorithm is monotonically increasing in posterior probability, with stable points of the iteration satisfying the necessary maximizer conditions of the maximum a posteriori solution. The algorithms were implemented on the DECmpp-SX, a 64 × 64 parallel processor, running at <2 s/(643, 3-D iteration). Results are demonstrated from simulated as well as amoebae and volvox data. We study performance comparisons of the algorithms for the missing-data problems corresponding to fast data collection for rapid motion studies in which every other focal plane is removed and for imaging with limited detector areas and efficiency.

© 1993 Optical Society of America

History
Original Manuscript: July 16, 1992
Revised Manuscript: December 7, 1992
Manuscript Accepted: December 10, 1992
Published: May 1, 1993

Citation
Sarang Joshi and Michael I. Miller, "Maximum a posteriori estimation with Good’s roughness for three-dimensional optical-sectioning microscopy," J. Opt. Soc. Am. A 10, 1078-1085 (1993)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-10-5-1078

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